Today I updated the analysis to include the absolute, final
vote totals as requested by another DUer. I had used the
preliminary results as of Nov 3, disregarding any changes to
the actual reported totals. The final numbers make the results
even more improbable, if that is possible.
I do request any enterprising DUer to check my numbers. If you
do, note that the vote and exit poll percentages have been
converted to their 2-party equivalents and add to 100%. If
there are errors in the updated voting percentages, please let
me know.
Now, here is the crux of the update.
In the original analysis,
1) 16 states deviated beyond the MOE to Bush.
The latest numbers now show that TWENTY (20) did.
The probabilities of this occurrence have gone beyond the
known universe. So unlikely, that Excel cannot compute it.
2) 41 states deviated to Bush, regardless of MOE.
The latest numbers now show that FORTY-THREE (43) did.
This reduces the probablity to one in 2.9 Million.
I will check the numbers again. I believe they are accurate.
Kerry's exit poll and vote percentages are based on the
exit poll numbers downloaded by Simon at 12:22 AM Nov 3.
The numbers have been converted to two-party percentages
so as to total 100%. The purpose was to maintain
comparability to other pre-election projection models. The
adjustments are proportional to the exit poll and vote
percentages. The post-adjusted numbers are in proportion to
the original numbers. There is NO BIAS for Kerry or Bush.
For example:
Assume Bush won the state vote 50%-49% with 1% going to third
parties.
Bush's adjusted two-party percentage is 50/99 = 50.505%
Kerry's two-party percentage is 49/99 = 49.495%
These are the relevant statistics from the table:
N = exit poll sample size
Poll = Kerry's exit poll percentage
Vote = Kerry's vote percentage
Diff = Kerry deviation from exit poll to vote
MOE = Margin of error = 1/sqrt(N)
StDev = standard deviation = MOE /1.96 (95% confidence level)
Prob = Probability of vote deviation based on Diff and StDev
Prob is calculated for each state using the Excel Function:
Prob = 1-Normdist(Poll, Vote, StdDev, true)
Odds = odds of occurrence = 1 in (1/Prob)
Analysis Summary
----------------
Bush vote tallies exceeded the exit poll MOE in 20 states.
The probability of this occurence is given by the Excel
formula:
Prob = 1- BINOMDIST(19,51,.025,TRUE)
The ORIGINAL odds of this occurring due to chance for SIXTEEN
(16) states was 1 in 13.5 trillion.
In the NEW analysis, for Bush's vote tallies to exceed the MOE
in TWENTY (20)states, it is BEYOND the CAPACITY of Excel to
display the result - because the probability is smaller than
30 ZEROS to the RIGHT of the decimal point. And Excel only
displays the result up to thirty decimals. It is therfore
effectively zero.
****** The probability is VIRTUALLY ABSOLUTE ZERO *********
I cannot calculate the odds, because you can't divide by
zero..
As previously mentioned, the final voting numbers show that
exit poll deviations without regard to the margin of error
favored Bush in 43 states.
The probability of this occurence is given by the Excel
formula:
Prob = 1- BINOMDIST(42,51,0.5,TRUE)
The odds of this occurring due to chance alone:
************** 1 in 2.9 MILLION *********************
Other stats:
The unweighted average Kerry deviation from the exit polls:
2.24%.
The unweighted average MOE for all states: 2.85%.
The MOE was significantly lower than the average (2.85%) in
the
battleground states where the sample size was large.
A total of 73,607 were polled nationwide.
St N Poll Vote Diff StDev MoE Prob 1 in >MoE? Favor
AK 910 40.5% 35.6% -4.9% 1.7% 3.3% 0.002 524 yes Bush
AL 730 41.0% 36.9% -4.1% 1.9% 3.7% 0.014 70 yes Bush
AR 1,402 46.6% 44.6% -2.0% 1.4% 2.7% 0.066 15 Bush
AZ 1,859 47.0% 44.4% -2.6% 1.2% 2.3% 0.014 72 yes Bush
CA 1,919 54.0% 54.4% 0.4% 1.2% 2.3% 0.645 2 Kerry
CO 2,515 49.1% 47.1% -2.0% 1.0% 2.0% 0.024 42 yes Bush
CT 872 58.5% 54.3% -4.2% 1.7% 3.4% 0.008 130 yes Bush
DC 795 91.0% 89.4% -1.6% 1.8% 3.5% 0.193 5 Bush
DE 770 58.5% 53.4% -5.1% 1.8% 3.6% 0.003 385 yes Bush
FL 2,846 50.5% 47.1% -3.4% 1.0% 1.9% 0.000 4,799 yes Bush
GA 1,536 43.0% 41.4% -1.6% 1.3% 2.6% 0.112 9 Bush
HI 499 53.3% 54.0% 0.7% 2.3% 4.5% 0.622 2 Kerry
IA 2,502 50.6% 49.3% -1.4% 1.0% 2.0% 0.091 11 Bush
ID 559 33.5% 30.3% -3.2% 2.2% 4.2% 0.067 15 Bush
IL 1,392 57.0% 54.8% -2.2% 1.4% 2.7% 0.056 18 Bush
IN 926 41.0% 39.3% -1.7% 1.7% 3.3% 0.150 7 Bush
KS 654 35.0% 36.6% 1.6% 2.0% 3.9% 0.792 1 Kerry
KY 1,034 41.0% 39.7% -1.3% 1.6% 3.1% 0.204 5 Bush
LA 1,669 44.5% 42.3% -2.2% 1.2% 2.4% 0.040 25 Bush
MA 889 66.0% 62.1% -3.9% 1.7% 3.4% 0.011 90 yes Bush
MD 1,000 57.0% 56.0% -1.0% 1.6% 3.2% 0.262 4 Bush
ME 1,968 54.7% 53.6% -1.2% 1.2% 2.3% 0.154 6 Bush
MI 2,452 52.5% 51.2% -1.3% 1.0% 2.0% 0.112 9 Bush
MN 2,178 54.5% 51.2% -3.3% 1.1% 2.1% 0.001 797 yes Bush
MO 2,158 47.5% 46.1% -1.4% 1.1% 2.2% 0.101 10 Bush
MS 798 43.3% 40.2% -3.0% 1.8% 3.5% 0.046 22 Bush
MT 640 39.8% 38.6% -1.2% 2.0% 4.0% 0.277 4 Bush
NC 2,167 48.0% 43.6% -4.4% 1.1% 2.1% 0.000 35,233 yes Bush
ND 649 34.0% 35.5% 1.5% 2.0% 3.9% 0.773 1 Kerry
NE 785 36.8% 32.7% -4.0% 1.8% 3.6% 0.013 75 yes Bush
NH 1,849 55.4% 50.4% -5.0% 1.2% 2.3% 0.000 94,466 yes Bush
NJ 1,520 55.0% 52.9% -2.1% 1.3% 2.6% 0.059 17 Bush
NM 1,951 51.3% 49.0% -2.3% 1.2% 2.3% 0.026 39 Bush
NV 2,116 49.4% 48.1% -1.3% 1.1% 2.2% 0.128 8 Bush
NY 1,452 63.0% 58.4% -4.6% 1.3% 2.6% 0.000 3,468 yes Bush
OH 1,963 52.1% 48.7% -3.4% 1.2% 2.3% 0.002 624 yes Bush
OK 1,539 35.0% 34.4% -0.6% 1.3% 2.5% 0.330 3 Bush
OR 1,064 51.2% 51.6% 0.4% 1.6% 3.1% 0.601 2 Kerry
PA 1,930 54.3% 51.0% -3.4% 1.2% 2.3% 0.002 566 yes Bush
RI 809 64.0% 59.6% -4.4% 1.8% 3.5% 0.007 147 yes Bush
SC 1,735 46.0% 41.0% -5.0% 1.2% 2.4% 0.000 52,161 yes Bush
SD 1,495 37.8% 38.4% 0.7% 1.3% 2.6% 0.697 1 Kerry
TN 1,774 41.5% 42.5% 1.0% 1.2% 2.4% 0.801 1 Kerry
TX 1,671 37.0% 38.2% 1.2% 1.2% 2.4% 0.837 1 Kerry
UT 798 30.5% 26.0% -4.5% 1.8% 3.5% 0.007 149 yes Bush
VA 1,431 48.0% 45.6% -2.4% 1.3% 2.6% 0.038 26 Bush
VT 685 65.0% 59.2% -5.8% 1.9% 3.8% 0.002 666 yes Bush
WA 2,123 54.9% 52.9% -2.1% 1.1% 2.2% 0.030 34 Bush
WI 2,223 52.5% 49.8% -2.7% 1.1% 2.1% 0.006 175 yes Bush
WV 1,722 45.3% 43.2% -2.1% 1.2% 2.4% 0.047 21 Bush
WY 684 30.9% 29.1% -1.8% 2.0% 3.8% 0.182 5 Bush
73,607
Avg 1,443 48.82% 46.58% -2.24% 1.46% 2.85% 0.1094 9 Bush
Med 1,495 49.10% 47.08% -2.09% 1.32% 2.59% 0.0474 21 Bush
Min 499 30.50% 26.03% -5.78% 0.96% 1.87% 0.0000 94,466
Max 2,846 91.00% 89.43% 1.62% 2.28% 4.48% 0.8372 1